Advertisement

Automation and Remote Control

, Volume 65, Issue 11, pp 1793–1799 | Cite as

A Finite MAP K /G K /1 Queueing System with Generalized Foreground-Background Processor-Sharing Discipline

  • C. D'Apice
  • R. Manzo
  • A. V. Pechinkin
Article

Abstract

Queuing systems with Markov arrival process, several customer types, generalized foreground-background processor-sharing discipline with minimal served length or separate finite buffers for customers of different types, or a common finite buffer for customers of all types are studied. Mathematical relations are derived and used to compute the joint stationary distribution of the number of customers of all types in a system.

Keywords

Mechanical Engineer System Theory Stationary Distribution Arrival Process Queueing System 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

REFERENCES

  1. 1.
    Schrage, L., The Queue M=G=1 with Feedback to Lower Priority Queues, Manag. Sci., 1967, vol. 13, no. 7, pp. 466–474.Google Scholar
  2. 2.
    Yashkov, S.F., Foreground-Background Processor-Sharing Service Discipline for Customers with Minimal Served Length, Tekh. Sredstv Svyazi, Ser. ASU, 1978, no. 2, pp. 51–62.Google Scholar
  3. 3.
    Pechinkin, A.V., Stationary Probabilities in a System with Foreground-Background Processor-Sharing Discipline, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1980, no. 5, pp. 73–77.Google Scholar
  4. 4.
    Schassberger, R., The Steady-State Distribution of Spent Service Times Present in the M=G=1 Foreground-Background Processor-Sharing Queue, J. Appl. Prob., 1988, vol. 25, pp. 194–203.Google Scholar
  5. 5.
    Nagonenko, V.A. and Pechinkin, A.V., High Traffic Intensity in a System with Foreground-Background Processor Sharing Discipline, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1980, no. 6, pp. 62–67.Google Scholar
  6. 6.
    Pechinkin, A.V. and Tatashev, A.G., Generalized Foreground-Background Processor Sharing Discipline, Izv. Akad. Nauk SSSR, Tekh. Kibern., 1981, no. 4, pp. 120125.Google Scholar
  7. 7.
    Yashkov, S.F., Analiz ocheredei v EVMs (Computer-aided Analysis of Queues), Moscow: Radio i Svyaz', 1989.Google Scholar
  8. 8.
    Pechinkin, A.V., Nestatsionarnye kharakteristiki SMO s distsiplinoi PRP (Time-Varying Characteristics of a Queueing System under FBPS Discipline), Sb. Veroyatnost' i ee prilozheniya. Mat. issledovaniya (Collected Papers on Probability and Its Application: Mathematical Investigation), Kishinev: Stiintsa, 1990, vol. 116.Google Scholar
  9. 9.
    Pechinkin, A.V., Stationary State Probabilities of a Queueing System with Markov Input Flow and FBPS Discipline, in Sb. Poisk signala v mnogokanal'nykh sistemakh (Search for Signals in Multichannel Systems), Tomsk: Tomsk. Gos. Univ., 1987, vol. 2, pp. 137–140.Google Scholar
  10. 10.
    Bocharov, P.P. and Pechinkin, A.V., Teoriya massovogo obsluzhivaniya (Queueing Theory), Moscow: Ross. Univ. Druzhby Narodov, 1995.Google Scholar
  11. 11.
    Lucantoni, D.M., New Results of the Single-Server Queue with a Batch Markov Arrival Process, Commun. Statist. Stochastic Models, 1991, vol. 7, pp. 1–46.Google Scholar
  12. 12.
    Lucantoni, D.M., Choudhury, G.L., and Whitt, W., The Transient BMAP=G=1 Queue, Commun. Statist. Stochastic Models, 1994, vol. 10, pp. 145–182.Google Scholar
  13. 13.
    Pechinkin, A.V., Stationary State Probabilities of theMAP=G=1=n System with Foreground-Background Processor Sharing Discipline, Vest. Ross. Univ. Druzhby Narodov, Ser. Prikl. Mat. Inform., 1998, no. 1, pp. 104–109.Google Scholar
  14. 14.
    Pechinkin, A.V., The BMAP=G=1= 1 System with Foreground-Background Processor Sharing Discipline, Avtom. Telemekh., 1999, no. 10, pp. 108–114.Google Scholar

Copyright information

© MAIK “Nauka/Interperiodica” 2004

Authors and Affiliations

  • C. D'Apice
    • 1
  • R. Manzo
    • 1
  • A. V. Pechinkin
    • 2
  1. 1.University of SalernoItaly
  2. 2.Institute of Information ProblemsRussian Academy of SciencesMoscow

Personalised recommendations